In contrast with an expanding nanoplasma defined by Ditmire et al (Phys. Rev. A 53 (1996) 3379),
in this paper we consider a natural quiescent (Q) nanoplasma which appears in ultrasmall Josephson
junction qubits with a cosine potential in the Hamiltonian. In terms of a complex dielectric
function, the conductivity of Josephson nanoplasma, which contains the contributions from the
displacement current and the tunnelling of Cooper pairs across the gap, corresponds to an
electromagnetic wave in a plasma. A resonant absorption (i.e. a Josephson quantum gate) operates
whenever the real part of the dielectric function is zero and ω=ω_p. These results
are generalized to the case where the displacement of a quantum of electron spin generates a quantum of
qudrupole moment. Thus, we define a quadrupolar qubit in the framework of a nanoplasma spintronics
based on the electron spin, rather than on electron charge. The new Schrödinger catlike states, and
the interplay between quantum tunnelling and quantum nanochaos (chaoson) are also discussed